Question: Rewrite as a simplified fraction. ${1.94\overline{1} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 1941.1111...\\ 100x &= 194.1111...\end{align*}}$ Subtracting the two equations, we have: ${900x = 1747}$ ${x = \dfrac{1747}{900}} \text{or} {1 \dfrac{847}{900}}$